The solar gravitational moments J2n are important astronomical quantities whose precise determination is relevant for solar physics, gravitational theory and high precision astrometry, and celestial mechanics. Accordingly, we propose in the present work to calculate new values of J2n (for n = 1, 2, 3, 4, and 5) using recent two-dimensional rotation rates inferred from the high-resolution Solar Dynamics Observatory / Helioseismic and Magnetic Imager helioseismic data spanning the whole solar activity cycle 24. To this aim, a general integral equation relating J2n to the solar internal density and rotation is derived from the structure equations governing the equilibrium of slowly rotating stars. For comparison purpose, the calculations are also performed using rotation rates obtained from a recently improved analysis of Solar and Heliospheric Observatory / Michelson Doppler Imager heliseismic data for solar cycle 23. In agreement with earlier findings, the results confirmed the sensitivity of high-order moments (n > 1) to the radial and latitudinal distribution of rotation in the convective zone. The computed value of the quadrupole moment J2 (n = 1) is in accordance with recent measurements of the precession of Mercury’s perihelion deduced from high precision ranging data of the MESSENGER spacecraft. The theoretical estimate of the related solar oblateness Δ⊙ is consistent with the most accurate space-based determinations, particularly the one from Reuven Ramathy High-Energy Solar Spectroscopic Imager/Solar Aspect Sensor.